## Does the pure motive determine the Voevodsky motive?

I do not quite understand the construction of Voevodsky motives yet. Let $$k$$ be a field (possibly not algebraically closed), $$X$$ be a connected smooth projective $$k$$-scheme. Does the motive of $$X$$ in the abelian category of pure numerical motives determine its Voevodsky motive? The coefficients are either $$\mathbb{Z}$$ or $$\mathbb{Q}$$ (the answer should address both). Please provide a reference.

## $p$-adic realisation of Kummer motive and Frobenius matrix

Suppose $$M$$ is an object in the abelian category of mixed Tate motives over $$\mathbb{Q}$$, and it is an extension of $$\mathbb{Q}(0)$$ by $$\mathbb{Q}(1)$$ $$$$0 \rightarrow \mathbb{Q}(1) \rightarrow M \rightarrow \mathbb{Q}(0) \rightarrow 0.$$$$ Suppose the Hodge realisation of $$M$$ is the one associated to $$\log u, u \in \mathbb{Q}^*$$, i.e. $$u$$ is a nonzero rational number. Suppose $$p$$ is an unramified prime of $$M$$, and in the $$p$$-adic realisation of $$M$$, what is the matrix associated to the geometric Frobenius?

The matrix must be of the form $$\begin{pmatrix} 1, ~~~0 \ *, 1/p \end{pmatrix}$$ but is the unknown $$*$$ in the matrix just the $$p$$-adic value of $$\log u$$, i.e. the $$p$$-adic logarithm valued at $$u$$.

Remark, I do not understand the $$p$$-adic realisations of the mixed Tate motives very well, so the statement of this question might not be very rigorous. References about the $$p$$-adic realisations of mixed Tate motives are welcomed.

## What is the motive behind this shockingly annoying decision by Youtube? [on hold]

I am trying to understand what motives a multi-billion dollar platform, that employs thousands of smart people to perfect its services, might have to make the decision to completely and utterly destroy the user experience.